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We consider a thin heterogeneous layer consisted of the thin beams (of radius$r$) and we study the limit behaviour of this problem as the periodicity$\varepsilon$, the thickness $\delta$ and the radius $r$ of the beams tend tozero. The decomposition of the displacement field in the beams developed in[Griso, Decompositions of displacements of thin structures, 2008] is used,which allows to obtain a priori estimates. Two types of the unfolding operatorsare introduced to deal with the different parts of the decomposition. Inconclusion we obtain the limit problem together with the transmissionconditions across the interface.

Homogenization via unfolding in domains separated by the thin layer of the thin beams